FIG. 1 shows a schematic diagram 100 of elements from a BICM (Bit Interleaved Coding and Modulation) module within a receiver in a digital communications system such as a Digital Terrestrial Television (DTT) system. The demapper 102 receives cells 104 and uses noise variance estimates 106 in order to output soft information 108 (which may also be referred to as soft estimates), such as Log-Likelihood Ratios (LLRs). This soft information 108 is passed to the decoder 110. In some examples, soft information is fed back to the demapper from the decoder (as indicated by dotted arrow 112) and this is referred to as iterative demapping or iterative decoding. In such an implementation, the soft information 108 output from the demapper 102 may be referred to as ‘extrinsic LLRs’ and the soft information which is fed back to the demapper from the decoder may be referred to as ‘a priori LLRs’.
Assuming that the transmitted data symbol is x and the received symbol is z, where the bit sequence [b0, b1, . . . , bi, . . . , bk] is mapped to symbol x and K is the number of bits mapped to the cell (which may also be referred to as a constellation symbol), the soft output 108 or LLR can be defined as:
                              L          ⁡                      (                                          b                i                            /              z                        )                          =                  ln          ⁢                                    p              ⁡                              (                                                      b                    i                                    =                                      0                    /                    z                                                  )                                                    p              ⁡                              (                                                      b                    i                                    =                                      1                    /                    z                                                  )                                                                        (        1        )            
The value of K varies depending on the constellation used, for example K=1 for BPSK (binary phase-shift keying) and K=8 for 256-QAM (quadrature amplitude modulation) constellation. The lower part of FIG. 1 shows an example 16-QAM constellation 120 for which K=4 and which shows the mapping of bit sequences to constellation points. This example uses Gray coding, such that successive sequences differ only by one bit.
In order to evaluate the LLRs, the demapper 102 typically uses a max-log approximation:
      L    ⁢          (                        b          i                /        z            )        =                    min                  x          ∈                      X            1                              ⁢              [                                                                                              z                  -                  x                                                            2                                      2              ⁢                              σ                2                                              +                                    ∑                              j                ,                                  j                  ≠                  i                                                      ⁢                                                  ⁢                                          b                j                            ⁢                                                L                  a                                ⁡                                  (                                      b                    j                                    )                                                                    ]              -                  min                  x          ∈                      X            0                              ⁢              [                                                                                              z                  -                  x                                                            2                                      2              ⁢                              σ                2                                              +                                    ∑                              j                ,                                  j                  ≠                  i                                                      ⁢                                                  ⁢                                          b                j                            ⁢                                                L                  a                                ⁡                                  (                                      b                    j                                    )                                                                    ]            where X0 and X1 are subsets of the constellation where bit bi=0 and bi=1, respectively. Additionally, La(bj) represents the a priori LLR value for bit bj that is passed from the channel decoder to the demapper, when iterative demapping is used. When no iterations are implemented, La(bj) is equal to zero.
In some scenarios, such as for DVB-T2, the constellation is not as shown in FIG. 1, but instead is rotated and Q-delayed. In such examples, the LLR calculation is done according to the following equation:
                              L          ⁢                      (                                          b                i                            /              z                        )                          =                                            min                              x                ∈                                  X                  1                                                      ⁢                          [                                                                                                                                                                  z                          I                                                -                                                  x                          I                                                                                                            2                                                        2                    ⁢                                          σ                      I                      2                                                                      +                                                                                                                                                    z                          Q                                                -                                                  x                          Q                                                                                                            2                                                        2                    ⁢                                          σ                      Q                      2                                                                      +                                                      ∑                                          j                      ,                                              j                        ≠                        i                                                                              ⁢                                                                          ⁢                                                            b                      j                                        ⁢                                                                  L                        a                                            ⁡                                              (                                                  b                          j                                                )                                                                                                        ]                                -                                    min                              x                ∈                                  X                  0                                                      ⁢                          [                                                                                                                                                                  z                          I                                                -                                                  x                          I                                                                                                            2                                                        2                    ⁢                                          σ                      I                      2                                                                      +                                                                                                                                                                                  z                            Q                                                    -                                                      x                            Q                                                                                                                      2                                                              2                      ⁢                                              σ                        Q                        2                                                                              ⁢                                                            ∑                                              j                        ,                                                  j                          ≠                          i                                                                                      ⁢                                                                                  ⁢                                                                  b                        j                                            ⁢                                                                        L                          a                                                ⁡                                                  (                                                      b                            j                                                    )                                                                                                                                ]                                                          (        2        )            where zI and zQ are the I (in-phase) and Q (quadrature-phase) components of the received symbol z and xI and xQ are the I and Q components of the constellation point x. Additionally, σI and σQ are the noise standard deviation in the I- and Q-directions.
The max-log approximation is then implemented by evaluating the distance metric
                                                  z            I                    -                      x            I                                      2              2      ⁢              σ        I        2              +                                                  z            Q                    -                      x            Q                                      2              2      ⁢              σ        Q        2              +            ∑              j        ,                  j          ≠          i                      ⁢                  ⁢                  b        j            ⁢                        L          a                ⁡                  (                      b            j                    )                    for all constellation points and then performing an exhaustive search to identify the minimum distance metric for each bit being ‘0’ or ‘1’ and performing the subtraction as in equation (2) above.
The embodiments described below are not limited to implementations which solve any or all of the disadvantages of known methods of demapping.